City Council Speaker Melissa Mark-Viverito is being accused of slashing an annual grant to a respected Puerto Rican institute by nearly half this year as retribution for the director’s unwillingness to publicly support convicted terror leader Oscar López Rivera’s starring role in the recent Puerto Rican Day Parade.

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Since Mark-Viverito took the helm of the council in 2014, CUNY’s Center for Puerto Rican Studies at Hunter College — headed by Edwin Melendez — has received $970,000 in discretionary funding each year.

But after a flap within the Puerto Rican community over the parade’s initial decision to honor López Rivera with a “National Freedom Hero” award, the center saw its funding cut to $500,000 for fiscal 2018, council budget records show.

“Melendez apparently refused to publicly defend the Puerto Rican Parade’s honoring of Oscar López Rivera,” Angelo Falcon, director for the National Institute for Latino Policy, wrote in a newsletter that first reported the funding cut on Friday.

“If anything, this shows the problems that such political funding can have: What Mark-Viverito gives, on the one hand, she can easily take away with the other if you don’t play ball with her,” he added.

Falcon told The Post that several people told him “Melissa was pissed off at [Melendez] and ‘boom!’ ”

At the same time, CUNY’s Dominican Studies Institute at City College — which has received the same funding as the Puerto Rican center for the past three years — saw its allotment continue at the $970,000 level in fiscal 2018.

Asked about the allegations of political retribution by Mark-Viverito, Melendez told The Post, “I have no comment.”

In an e-mail response to Falcon, Melendez confirmed the funding cut without addressing the issue of political payback.

“We have learned that this City Council allocation has been reduced for the next fiscal year, which begins on July 1, 2017. Our core services will continue unaffected,” Melendez wrote in the e-mail. “We will continue to identify sources of funding that will permit Centro to continue offering the engagement and dissemination activities to the community in accordance to our mission.”

A City Council spokeswoman did not address the allegations directly, saying instead the council was proud to support CUNY research initiatives.

“Our $2.14 million in funding, which includes the addition of the newly funded Haitian and Mexican Studies Institutes, will continue to give students the resources to make the most of their studies and to support important research on these diverse communities,” the spokeswoman said.